Algorithm1. The k-means clustering algorithm

$Initialize n_i,i=1,\dots k,to k random x^{t }$ Repeat $For all {\mathrm{x}}^{\mathrm{t}}\in X$ ${\mathrm{b}}_{i \leftarrow \{\begin{array}{c}1 if\left|\left|x^1-n_i\right|\right|=mi{n}_j\left|\left|x^t-n_j\right|\right|\\ 0 otherwise\end{array}}^{\mathrm{t}}$ $\mathrm{For}\mathrm{all}{n}_i,i=1,\dots ,k$ $n_i\leftarrow {{\displaystyle \sum }}_t{b}_i^t{x}^t/{{\displaystyle \sum }}_t{b}_i^t$ $Until m_i converge$